Analysis of steady-state performance for cross-directional control

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Analysis of steady-state performance for cross-directional control

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The authors analyse the steady-state behaviour of a class of cross-directional controllers that are pertinent to general web-forming processes. Their analysis is framed in terms of the controllable space prescribed by the interaction matrix and general discrete orthonormal basis descriptions of both the input and output space under the assumption of closed-loop stability. The specific choice of controller defines (whether explicitly or implicitly) an additional assumed controlled space. It is well known that the controllable space determines a lower bound on output variation. They examine the implications of integral action and provide sufficient conditions for the steady-state output variation to achieve this lower bound. They confirm some intuitive results that connect the optimal constrained and unconstrained steady-state solutions for model-based control with no model mismatch. Model mismatch is usually detrimental to steady-state performance. This effect is interpreted in terms of leakage between the controllable and assumed controlled spaces, as well as their respective orthogonal complements.

Inspec keywords: stability criteria; forming processes; transfer function matrices; discrete time systems; closed loop systems; control system analysis; singular value decomposition; process control; predictive control

Other keywords: closed-loop system; web-forming processes; general discrete orthonormal basis descriptions; model-based control; model mismatch; closed-loop stability; discrete-time linear time-invariant models; orthogonal complements; leakage; singular value decomposition; optimal constrained steady-state solutions; sufficient conditions; steady-state performance; optimal unconstrained steady-state solutions; output space; steady-state output variation; integral action; steel rolling mills; paper-making machines; cross-directional control; transfer function matrix; interaction matrix; input space; controllable space; plastic film extrusion systems

Subjects: Stability in control theory; Control system analysis and synthesis methods; Control applications in manufacturing processes; Algebra; Optimal control; Discrete control systems; Forming processes; Algebra; Control technology and theory (production)

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